Ground states for Schrödinger–Kirchhoff equations of fractional [formula omitted]-Laplacian involving logarithmic and critical nonlinearity

Abstract

For 0<s<1<p<N/s and a parameter λ>0, we consider a class of Schrödinger–Kirchhoff equations of fractional p-Laplacian involving logarithmic nonlinearity and critical exponential growth: mup−Δpsu+Vxup−2u=λhxuθp−2ulnu+σups∗−2uinRNwith u=∫R2Nux−uypx−yN+spdxdy+∫RNVxupdx1/p,where ps∗=Np/N−sp, 1≤θ<ps∗/p, σ∈0,1, m(⋅) is a Kirchhoff function, V is a Rabinowitz potential, and h is a positive bounded perturbation. By using concentration-compactness principle and minimax argument, we prove the existence of a non-trivial ground state solution for λ sufficiently small.